00:01
In this problem, it is said that x is uniformly distributed over 0 .1, we need to calculate the expected value of x squared.
00:07
So, x is uniformly distributed over 01.
00:11
So let us consider the probability density function f of x.
00:15
Now, if we have a uniform distribution over ab, then it will be 1 by b minus a.
00:21
So in this case, it will be 1 by 1 minus 0.
00:24
B minus a, so 1 minus 0 for 0 less than x, less than 1.
00:29
This is how we write the probability density function, 1 by b minus a for a less than x less than b.
00:35
And it will be 0 otherwise.
00:40
So here we have 1 by 1 minus 0.
00:42
That's 1 by 1 which is just equal to 1.
00:44
So we have 1 for 0 less than x less than 1 and it will be 0 for everything else.
00:52
So we have been asked to find the expected value of x square.
00:57
I need to find the expected value of x square.
01:03
So that will be the integral of x square times fx vx.
01:12
So here we can see that fx is from 0 to 1.
01:17
It has one value and it has another value otherwise.
01:20
So we can just split this for minus infinity to 0.
01:24
We have that.
01:26
And then we have another integral from 0...